The accepted Lean release records complete mappings for all 87 registered proposition cores. Its scope is stated proposition by proposition in Lean/COVERAGE.md and Lean/COVERAGE.json. Each plate selects a mechanism from those statements.
| Plates | Proof route | Primary entry modules in Lean/KomorebiLSM/ |
|---|---|---|
| 1–2 | Reconstruction and transport | Realization, Normed |
| 3–4 | Closure and completion | PredictiveClosure, LinearClosure, InvariantCompletion |
| 5–6 | Packets and return paths | PacketTree, Transfer, Polynomial, LinearClosure |
| 7–8 | Memory and error propagation | Memory, MemoryBounds, MemoryStability, DefectPropagation |
| 9–10 | Observable and behavior states | Exact P14–P17 and P27–P28 entries in COVERAGE.json |
| 11–12 | Probability witnesses | PositiveLift, RotationP46, MatrixEmbedding, MatrixRotation |
| 13–14 | Integration and curved moments | Exact P57–P58 and P83 entries in COVERAGE.json |
| 15–16 | Confidence and horizon bounds | RegressionConfidence, StructuredLearningCapstone, MarkovMarginals |
A small notation key. \(A,S\) denote analysis and synthesis; \(\mathcal C={\operatorname{im}} A\) denotes realizable coefficients; \(\gamma\) denotes a predictive summary; \(P,Q\) denote retained and discarded projections; \(W_*\) denotes the completed observable row space; \(C\) denotes a probability cone in the stochastic plates; \(\lambda\) denotes its mass map. Symbols local to a plate are introduced there.
Evidence boundaries. Written proofs, exact example calculations, kernel verification, and statistical statements are separately identified. The formal release verifies the registered mathematical cores under their hypotheses. It does not empirically authenticate a model class, noise assumption, sensor or physical process.
Reproducibility. The companion includes the editable LaTeX source, Python figure generator, exact rational example receipt and a proposition/module map. All illustrations are mathematical diagrams or declared analytical calculations. The original volume remains the source of the full statements and proofs.